A sector with an area of 48 pi cm2 has a radius of 16 cm.
What is the central angle measure of the sector in radians?

Step-by-step explanation:

The area of a circular sector is defined as

Where is the central angle and is the radius of the circle.

Replacing given values, we have

But, this angle is in degrees, we know that

Therefore, the right answer is D.

Step-by-step explanation:

Area of a sector is expressed as

r is the radius of the circle

is the angle substended by the sector

Given Area of a sector = 48πcm²

radius of a circle = 16cm

Substituting the given values in the formula to get we have;

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step-by-step explanation:

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis: